chapter 6 notes
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Calculus
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Pre-calculus Semester One Troublesome Topics
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Prerequisite Skills Solving for x with absolute values Get rid of the absolute value signs by setting everything within absolute value to the opposite keeping the original equation Solve per usual Simplifying with square roots in the denominator Multiply the top and bottom by the square root on the bottom The square root number is no longer a square root and becomes the ?normal? form Reduce square roots to simplest form Solve per usual Chapter One Skills Finding the formula for f^-1(x) Switch the x and y values and solve per usual Altering graphs If f(x) is a function? f(x)-1 graph is shifted down one unit f(x)+1 graph is shifted up one unit f(x-1) graph is shifted right one unit f(x+1) graph is shifted left one unit
Calculus
P4 part P5 Test
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P4 and Part P5 Test Block_____ Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Multiply and reduce to lowest terms. 1) 2z 3 4 ? 28 z 2 A) 14z B) z 14 C) 14z 2 z 3 D) 14 z 1) 2) k 2 + 7k + 12 k 2 + 10k + 21 ? k 2 + 7k k 2 - 2k - 24 A) 1 k - 6 B) k k - 6 C) k k 2 + 10k + 21 D) k 2 + 7k k - 6 2) 3) y 2 - 25 7y + 35 ? y - 3 y - 5 A) 1 7 B) y - 3 7 C) (y - 3)(y - 5) 7(y - 5) D) y - 3 3) Divide and reduce to lowest terms. 4) 9x 2 - 64 x 2 - 64 ? 3x + 8 x + 8 A) 3x - 8 x - 8 B) x - 8 3x - 8 C) (3x + 8)(9x 2 - 64) (x 2 + 8)(x + 8) D) 3x + 8 x + 8 4) 5) y 3 - 5y y 2
First derivatives
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The first derivative of a function can tell a lot about how the original function looks. The first derivative tells us the critical numbers, and when the original function is increasing or decreasing.
Finding the critical numbers of a function is easy. You have a critical number anytime the derivative function equals 0, or if it does not exist. Critical numbers in the derivative usually tell us that there is a minimum, maximum, or a vertical asymptote. However, it does not guarantee a min/max.
Trig. Function Derivatives: sine, cosine, and tangent.
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The derivatives of the basic trig. functions are as follows:
f(x)=sin(x) / f`(x)=cos(x)
f(x)=cos(x) / f`(x)=-sin(x)
f(x)=tan(x) / f`(x)=sec^2(x)
derivatives
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dx/dy= derivative of function
Limits Formulas
Formula List for Extrema
homework
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Newton?s Method Test Questions Multiple Choice 1. Using Newton?s Method, evaluate to the 5th exact decimal. Show your work. A. 8.46515 B. 2.10154 C. 8.56511 D. 2.09715 2. Find starting with = 1, find the fourth approximation to the sixth decimal place. A. 3.847535 B. 1.820564 C. 3.096281? D. 3.215625 Free Response 3. A car dealer sells a new car for $18,000. He also offers to sell the same car for payments of $450 per month for four years. What monthly interest rate is this dealer charging? The formula for the present value is given by A = [1-]. Use Newton?s Method to solve this equation and show your work. (Hint: A = $18,000, R = $450, n = 48 & replace i with x). Interest rate 0.7701% Monthly
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